The object below is made of four rectangular prisms, each with dimensions of 75 centimeters (cm) by 30 cm by 20 cm. What is the volume, in cubic centimeters, of the object?

Question

Responses

180 , 000 cm . 3

45 , 000 cm . 3

11 , 400 cm . 3

9000 cm . 3

Answer 1

To find the volume of the object made of four rectangular prisms, we first calculate the volume of one prism.

The formula for the volume \( V \) of a rectangular prism is: \[ V = \text{length} \times \text{width} \times \text{height} \]

Given the dimensions:

• Length = 75 cm
• Width = 30 cm
• Height = 20 cm

We can calculate the volume of one prism: \[ V = 75 , \text{cm} \times 30 , \text{cm} \times 20 , \text{cm} \] First, calculate \( 75 \times 30 \): \[ 75 \times 30 = 2250 , \text{cm}^2 \]

Next, multiply by 20 cm: \[ 2250 , \text{cm}^2 \times 20 , \text{cm} = 45000 , \text{cm}^3 \]

So, the volume of one rectangular prism is \( 45000 , \text{cm}^3 \).

Since the object is made of four such prisms, the total volume of the object is: \[ 4 \times 45000 , \text{cm}^3 = 180000 , \text{cm}^3 \]

Therefore, the volume of the object is \( \boxed{180000 , \text{cm}^3} \).